Isotropic fluid-saturated microcracked rocks exhibit anisotropic response at the time of measurement

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Abstract
To bridge seismic P- and S-wave velocities and attenuation across the scales, two experimental techniques were found to capture rocks’ dissipative character and complex moduli: (i) the resonant-bar and (ii) the stress–strain forced-oscillation methods. Although none of these methods could directly measure P- and S-wave velocities, their inference had not been questioned: If the fluid-saturated rock was isotropic, any solicitation mode would yield properties that are still isotropic, and only two independent constants are required. In practice, however, reported laboratory data in undrained isotropic sandstones — when three independent complex elastic properties were measured under the same stress states — revealed inconsistencies that challenged this view. Undrained bulk moduli measured from hydrostatic oscillations Kudiso were significantly lower than those inferred from axial oscillations Kudax, although the dry rock showed Kdax∼Kdiso. This discrepancy existed in microcracked sandstones only at lowest effective pressures Peff and was related to anomalously high Poisson’s ratio νud when compared with well-validated inclusion theories. Most reported νud worldwide for microcracked rocks at low Peff highlighted the same inconsistency. Although the well-known concept of “static” stress-induced anisotropy was invalidated by Kdax∼Kdiso, what if a directional measurement induces a “dynamic” stress-induced anisotropy? A fully coupled 3D finite-element model incorporating compliant cracks, with either hydrostatic or axial loading and a simple geometry, was designed to check this question. Although it yielded Kdax∼Kdiso under dry conditions, Kudax was 25% larger than Kudiso under liquid saturation. The undrained mechanical response of an isotropic microcracked rock might have been that of an anisotropic rock at the time of the measurement if the loading method itself was anisotropic.

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